Mathematics

Problem

Let

f:\mathbb R\to\mathbb R

be defined by

f(x)=2\,(x-3)^2-4

. a. (i) Find the coordinates of the vertex of the parabola represented by

y=f(x)

. b. (ii) Determine the

x

-intercepts and the

y

-intercept of the graph. c. (iii) Sketch the graph of

y=f(x)

, clearly showing the vertex, axis of symmetry, intercepts and the direction of opening. d. (iv) From the sketch, write the domain and range of

f